Stir remaining white chocolate in top of double boiler over barely simmering water until melted and smooth. Using small spoon, drizzle about half of melted chocolate in thin lines over cooled cookie. Sprinkle remaining crushed peppermint candies over chocolate. Drizzle remaining white chocolate over top. Let stand until white chocolate sets, about 1 hour. Break cookie into irregular 2- to 3-inch pieces. DO AHEAD Can be made 2 days ahead. Store in airtight container at room temperature.